Nebenwinkel ergeben zusammen 180°.

$\alpha +\beta ={180}^{\circ }\backslash alpha+\backslash beta=180^\backslash circ$

$\beta \backslash beta$ ist ${80}^{\circ }80^\backslash circ$ größer als $\alpha \backslash alpha$.

$\beta =\alpha +{80}^{\circ }\backslash beta=\backslash alpha+80^\backslash circ$

$\begin{array}{c}\\ \alpha +\beta =\alpha +(\alpha +{80}^{\circ })={180}^{\circ }\\ 2\alpha +{80}^{\circ }={180}^{\circ }\\ 2\alpha ={100}^{\circ }\\ \alpha ={50}^{\circ }\end{array}\backslash def\backslash arraystretch\{1.25\}\; \backslash begin\{array\}\{l\}\backslash \backslash \backslash alpha+\backslash beta=\backslash alpha+(\backslash alpha+80^\backslash circ)=180^\backslash circ\backslash \backslash 2\backslash alpha+80^\backslash circ=180^\backslash circ\backslash \backslash 2\backslash alpha=100^\backslash circ\backslash \backslash \backslash alpha=50^\backslash circ\backslash end\{array\}$

Das Winkelmaß von $\alpha ={50}^{\circ }\backslash alpha=50^\backslash circ$.